Space of modular forms of level 5070, weight 2, and Character 5070.b

• Label: 5070.2.b
• Level: $5070$
• Weight: $2$
• Character orbit: 5070.b
• Rep. character: $\chi_{5070}(1351,\cdot)$
• Character field: $\Q$
• Dimension: $100$
• Newform subspaces: $27$
• Sturm bound: $2184$
• Trace bound: $22$

Defining parameters

Level:	\( N \)	\(=\)	\( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5070.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 27 \)
Sturm bound:			\(2184\)
Trace bound:			\(22\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\), \(31\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(5070, [\chi])\).

	Total	New	Old
Modular forms	1148	100	1048
Cusp forms	1036	100	936
Eisenstein series	112	0	112

Trace form

100 * q + 4 * q^3 - 100 * q^4 + 100 * q^9 - 4 * q^10 - 4 * q^12 - 8 * q^14 + 100 * q^16 - 8 * q^22 - 100 * q^25 + 4 * q^27 - 16 * q^29 - 4 * q^30 - 8 * q^35 - 100 * q^36 + 32 * q^38 + 4 * q^40 + 8 * q^42 - 16 * q^43 + 4 * q^48 - 52 * q^49 - 8 * q^55 + 8 * q^56 - 40 * q^61 + 16 * q^62 - 100 * q^64 - 8 * q^66 + 16 * q^69 - 8 * q^74 - 4 * q^75 + 80 * q^77 - 16 * q^79 + 100 * q^81 - 16 * q^87 + 8 * q^88 - 4 * q^90 - 32 * q^94 - 32 * q^95

Decomposition of \(S_{2}^{\mathrm{new}}(5070, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5070.2.b.a	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots\)
5070.2.b.b	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.e	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots\)
5070.2.b.c	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}-i q^{5}+i q^{6}+\cdots\)
5070.2.b.d	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.f	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}-i q^{5}+i q^{6}+\cdots\)
5070.2.b.e	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.e	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.f	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.b	$2$	$1$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.g	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.h	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.f	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}-q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.i	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.j	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.c	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}+i q^{5}+i q^{6}+\cdots\)
5070.2.b.k	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					30.2.a.a	$2$	$1$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+q^{3}-q^{4}-i q^{5}-i q^{6}+\cdots\)
5070.2.b.l	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.i.d	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+q^{3}-q^{4}-i q^{5}-i q^{6}+\cdots\)
5070.2.b.m	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.d	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{3}-q^{4}-i q^{5}+i q^{6}+\cdots\)
5070.2.b.n	$5070$	$2$	5070.b	13.b	$2$	$2$	$2$	$40.484$	\(\Q(\sqrt{-1}) \)	None					390.2.a.g	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{2}+q^{3}-q^{4}+i q^{5}-i q^{6}+\cdots\)
5070.2.b.o	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{12})\)	None					390.2.bb.b	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}-q^{3}-q^{4}+\beta_1 q^{5}-\beta_1 q^{6}+\cdots\)
5070.2.b.p	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{12})\)	None					390.2.bb.a	$2$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}-q^{3}-q^{4}+\beta_1 q^{5}+\beta_1 q^{6}+\cdots\)
5070.2.b.q	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(\zeta_{8})\)	None					390.2.a.h	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_1 q^{2}+q^{3}-q^{4}-\beta_1 q^{5}-\beta_1 q^{6}+\cdots\)
5070.2.b.r	$5070$	$2$	5070.b	13.b	$2$	$4$	$4$	$40.484$	\(\Q(i, \sqrt{17})\)	None					390.2.i.g	$2$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
5070.2.b.s	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bk	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.t	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bj	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.u	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bm	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.v	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bl	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.w	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bo	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}+\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.x	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bn	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}-\beta _{5}q^{6}+\cdots\)
5070.2.b.y	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bq	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.z	$5070$	$2$	5070.b	13.b	$2$	$6$	$6$	$40.484$	6.0.153664.1	None		✓			5070.2.a.bp	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+q^{3}-q^{4}-\beta _{5}q^{5}+\beta _{5}q^{6}+\cdots\)
5070.2.b.ba	$5070$	$2$	5070.b	13.b	$2$	$8$	$8$	$40.484$	8.0.\(\cdots\).1	None			✓		390.2.bb.c	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(5070, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(5070, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(845, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1690, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2535, [\chi])\)\(^{\oplus 2}\)